From my experience, it has to be locked, or would be unavailable for trade.
I hadto learn the hard way due to my slight impatience and fatigue for grinding, but got one for SE when I used PU and unlocked it anyway. Thought I was stuck, but was lucky to see that a person was selling it for my class, so I paid 40G for it -30G from the SE outfit I sold. You do have another chance to get another depending from when you opened the loot box. :3